Cosmology has been treated as a poor relation. Here we shall study it for itself, according to its own logic—which is not exclusive to cosmology—without bringing in the question of the relation it necessarily maintains with the successive interpretations of ἔστι (“is”) in fragment 8. [1] The status that has been assigned to cosmology is not unrelated to the stagnation into which the discussion has sunk within a false debate, and which is in large measure responsible for the (more than relative) scorn that the cosmological portion of Parmenides’ poem has incurred, by virtue of a disdain that was thought to be attributable to its author, in an objectivization of that critical disdain. Perceptible bodies were viewed as less worthy. Parmenides’ suspicion regarding matter inevitably lent support to the suspicions brought to bear on the texts that inform us, as it turns out, about the physical system of the cosmos.

Now, the possibility of a reconstitution is quite high. The solid, detailed, and structured summary preserved in Aetius (28 A 37 D-K) allows us to rediscover and retrace with precision the phases in the constitution of the world, with the ultimate outcome being a complete theoretical elucidation. As the details are fleshed out, the process can be conceptualized. The original fragments on matter cited by Simplicius are clarified in the context of the doxographic fragment from Theophrastus (46 A D-K). [2] The latter is precise enough, and at the same time broad enough, for the elements of which the original fragments are composed to be identified in it and to contribute a complement to the skeletal interpretive framework that, with the help of a general outline, makes it possible to integrate the specimens of the lost achievement. The testimonies corroborate one another remarkably well.

The doxa of the unintelligible

The confusion in the doxographic narratives is set up as authoritative by a consensus among scholars: “It is generally acknowledged that the accounts are full of contradictions and do not offer a coherent doctrine” (Gigon 1945:276). [3] Burkert (1962) draws up a list that can be extended. [4] The detailed interpretation can remain in suspense. One does what one wishes with “open” material. Raven made the clearest pronouncement (in Kirk-Raven 1957:284): “It is fortunate that, since he [Parmenides] neither believed in it himself [the tradition of Diels, Burnet, and so on] nor, apparently, succeeded in influencing others by it [the singularity is turned back against the author], Parmenides’ astronomical system [the precondition for the expectation to be satisfied] is of little importance [this is the common opinion; see Guthrie and others]; for it is virtually impossible to reconstruct [reconstruction is not worth attempting; thus by default it supplies proof of its lack of interest; the verdict is ‘circular’].”

For Karsten (1835:243), Parmenides had not gone into detail; he had settled for a “poetic” sketch (universi specie adumbrate [“representing a fictitious universe”]). Zeller (1855:482–483) saw Parmenides as interested “in the research of his day,” adhering to the Pythagorean world system without following it in all respects. [5]

In 1901, Diels made a note regarding fragment 12, at the beginning of his critical edition: nondum prorsus explicatum (“not yet precisely explained”). In his positivist faith, he believed that time would do the rest.

The lack of coherence of the account in Aetius (A37) does not have the same function for all the authors who have cited it. Either the testimony is rejected altogether as unintelligible, as it is by Guthrie (1965), for whom it justifies agnosticism, or else the verdict of incoherence has to allow for a free reconstruction. Scholars feel authorized to accommodate all the arrangements that the restoration “according to Parmenides” calls for. The analysis of the options will necessarily oscillate between an element of scientific discussion, on the basis of the premises (and prejudices) that the author is trying to advance, and another more personal element that sets science aside and rules out discussion.

For Guthrie, too, Aetius’ incoherence is accompanied by a more basic lack of interest. The material is lost; this is not too serious, because Parmenides had treated the topic of cosmology as if it were a duty, trying to improve what he was reading in Anaximander or in the Pythagoreans; [6] it was only “a deliberate concession to human weakness; his contribution to philosophy lay elsewhere” (p. 61). Thus the author refrains from trying to elucidate the texts, preferring to limit himself, since the material does not properly belong to Parmenides, [7] to approximate correspondences to the Ionian and Pythagorean systems and their reflections in Plato’s work. The references offer only potential comparative models.

There is nothing to be drawn “from this garbled and confused summary” (Guthrie 1965:62). Confused: this is how Aetius’ narrative strikes many others (Mansfeld 1984, for example), even though he accepts the distinction between cosmogony (according to Reinhardt; see below, Aetius A 37 D-K) and cosmology. [8]

The very lengthy discussion of cosmology by Tarán (1965) is particularly disappointing, although it is instructive if one considers the common preconceptions of critical examination; these preconceptions differ in Tarán’s case because their application is pushed to the point of mechanical caricature. At the expense of any signifying construction by a language, a language that would be inherent in the design of an abstract structure, Tarán limits himself to the appearance produced by the sensory experience of the world, supplying a horizon of expectation that Parmenides is presumed to have shared with him. [9] Parmenides is thus not read in order to be discovered, but rather to be confronted with what the reference to “reality” makes it probable that he meant. [10]

The texts, and in particular Theophrastus’ summary, are systematically deprecated because they do not meet this expectation. The difficulty of finding in the text itself the physical representation that the text is supposed to be reproducing does not lead to a re-examination of the hypothesis, as the laws of hermeneutics, or more generally of scientific practice, would require; the information is viewed as suspect before it is studied on its own terms. Tarán fits into a tradition represented by Cherniss (1935) or, for Theophrastus, by McDiarmid (1953), in which an older skepticism about sources has been generalized, to the extent that non-comprehension attributed to authors such as Aetius of what is being reported on (and contaminated) is elevated to the rank of criterion. The difference between the anticipated meaning and the content of the doxographic account studied is projected (and objectivized) in the irreducible distance of a primary inadequacy at the level of the source. What is not understood by the interpreter is presumed not to have been understood by the author. [11]

Reinhardt’s “cosmogonic” hypothesis (1916) has often been ignored, as if it were being censored, and deemed mystifying. It is thus neither discussed nor refuted. Tarán does mention Reinhardt’s hypothesis several times, but as a forbidden path, excluded a priori. [12]

The impasse of composite constructions

To be able to harmonize the entirety of Aetius’ text and Parmenides’ fragment 12 [13] with the description of the world as it had come into being, Diels (1897) introduced a whole series of interpretive and critical operations. He had the solid firmament (1) on the upper level, and the layer of fire, the ether below (2), followed by astronomic “spheres” of a composite nature, that is, blended with night; in each of its wheels there is fire, through which the celestial bodies were designated (3). [14] There was no concern for relative proportions, which were to the benefit of night; [15] in fact, the equivalence or relation between masses was not perceived, despite the undeniable parallelism, as an objective of the construction. One also sees that the “crowns” were used, on the one hand, as layers that could represent the parts of the world and, on the other, as cylindrical rings (on the model of Anaximander’s wheels), conceived as the dwelling spaces of the planets or of the Milky Way.

Nothing is situated between these astral rings and the earth. The atmosphere, the sublunar region, is lacking. However, since the earth cannot in reality be enveloped by pure fire, Diels corrected Aetius’ text, introducing an “underneath” (ὑφ’ ᾧ) so as to be able to situate, under the terrestrial envelope (4), a central fire (5), [16] about which it could easily be said that, in this form, it had virtually no analog in any other doctrine of physics. [17]

This outline formed the point of departure for the cosmological discussion starting in the early twentieth century, thanks to the authority of Diels’ publications. The other explanations are variations, infinite in number, sometimes minimal, reduced to a single, immutable principle of adaptation. [18] Fränkel distanced himself to a greater degree from Aetius (who was considered beyond recuperation) by freely sketching a degraded loss of the igneous purity of the border areas (a. the pure fire of the ether, below the envelope; b. the blended zone, starting with the Milky Way; c. the terrestrial region). [19]

Without a real analysis of the problems of the “crowns,” Karsten (in 1835, two generations before Diels) had divided the world rationally into three parts. Fire was confined to the upper regions; the rampart itself consisted of fire (see Gigon 1945), in “Olympus” and the sky and the region of fixed bodies; the terrestrial region was at the other extreme; between the two, there was mixed matter in the ether, with the planets and the Milky Way, which made it possible to find the astronomers’ spheres again, and to give a meaning to the mysterious “crowns.” In Karsten’s view, the idea that Parmenides had gone very far in this study of the sky remained doubtful. [20]

The most rudimentary reduction was more bipartite: a ring of fire above, another of night below; between the two, [21] a sphere blended with the goddess.

Given the uncertainties of the critics, Couloubaritsis (1986) chose to superimpose the schemas in cosmic space, basing his decision on a global entanglement (see περιπεπλεγμένας, A 37 [“intricate, complicated”]); [22] he could accept a cosmogonic reading (frags. 11, 12), inserted in a static cosmological analysis, articulated around a point considered to be the origin of movement and leading toward the center. [23] The seat of the she-daimon and the theogony that proceeds from it are “mythical”; within the same system, mixed circles, situated below the she-daimon’s seat, belong to a phenomenal or physical order; the passage from one order to the other is made through the figure of the goddess. [24]

The succession of the spheres (in a free, unjustified order), for which Couloubaritsis juxtaposes (without studying their relationship) A 37 and B 12, even though the texts bear on exactly the same object, is localized in an upper part of the world, exempt from becoming, which would begin in a center, amid the mixed crowns (in this case, one would have to acknowledge with Couloubaritsis that the blend preexisted, in a non-dynamic form, below the periphery). The milieu of all the crowns, in the upper part of the world, and the seat of the goddess, at the center of the mixed crowns (according to A 37 and B 12), were for him two distinct places. All of astronomy (even the fixed bodies of the vault) thus had to be situated below the center of the mixed elements. If one were to extract the elements of the reading (they are there) from this free and “synchronic” construction, one would have a way to reread the texts and to decipher the reference on that basis. The construction belongs to the author alone, apart from any possible debate. Immobility does not coexist with movement in one part of the world; the blend is not partially immobile, and so forth.

The problem of the igneous zone surrounding the earth

When the “rings” are reserved for the journeys of the celestial bodies, in a cosmological interpretation of Aetius’ account, we go no further down than the moon. If we insist on a minimum of coherence, we cannot put the terrestrial sphere or the envelope of the fixed bodies on the same plane as the moon, [25] nor can we consider the system to be complete. If we stick to a narrow interpretation of the system, it is interrupted (it has a hole in it, in Diels’ account), but even in a broader interpretation it is no less interrupted. [26] Yet another instance of incoherence.

Diels eliminates the problem by correcting the text. Fire is relegated to the inside. Other authors, the majority, end the description at the height of the moon, leaving the intermediate space blank. But even in this case the authors have to eliminate the alternation in order to progress, from the “heavens” to the moon, toward an increase in the nocturnal element. Fränkel manages this through a critique of Theophrastus’ reading of Parmenides (frag. 12), [27] anticipating the method practiced to the point of caricature by Tarán. In fact, Fränkel eliminates a meaning that is approximately accurate, [28] considering it an error on Theophrastus’ part, in favor of an erroneous match with reality, drawn from the fragment. [29] The aporia is eliminated mechanically. A first series of astronomical “spheres” is of pure fire; a second, increasingly clouded and dirty (Fränkel 1951:413), culminates in a point of lunar ambiguity announcing the world of men. “Mixed” takes on a deprecatory connotation.

It is hard to know whether the physical system, as constructed by these scholars, is the source of the theories on the status of the doxa, or whether it is the other way around. When, for Untersteiner (1958), the doxa is distinguished from the “eon” by the fall into temporality, the instruments for measuring time in the sky become essential; a confirmation of this opinion is found in the astronomical spheres, which are thought (or said) to occupy a new place in Parmenides. [30]

Non-mixing (frag. 9)

The principle of non-sharing is formulated in fragment 9, based on the rigorous autonomy of Day and Night.

The opposition, which forms the basic structure found in everything, stems from the constitutive contrary tensions of the figure of the represented Being. Before they were elements in the narrow sense of the term, Aristotle’s fire and earth, the principles of Light and Night were witnesses to the division of Being as it appeared. The first designates the centrifugal impulse, the second the centripetal impulse. The attributes of lightness and heaviness, sparseness and density, express and develop this identification. In fact, the identity of each of these principles excludes the identity of the other. Rigorously equivalent, if one sets aside the non-contradictory and supernumerary attribute of softness (ἤπιον), which gives Light an advantage that is hard to measure, the cosmic powers divide up the universe and are present in all the intermediate concrete manifestations of the real.

Since all things have been named light and night and also according to the forces belonging to the one and the other, in the case of such things as well as of such others, everything is full together of light and of night without light, the two being equals, because neither one contains anything of the other.

Since all things have been named light and night and also according to the forces belonging to the one and the other [the group τὰ κατὰ σφετέρας δυνάμεις (“the forces. …”) designates the qualities associated with the principles; it is an attribute of πάντα, on the same basis as φάος and νύξ], [31] in the case of such things as well as of such others (the prepositional group is not a complement of ὀνόμασται but it determines δυνάμεις [32] ), everything is full together [ὀμοῦ does not express simultaneity but rather contiguity [33] ] of light and of night without light, the two being equals, because neither one contains anything of the other. The causal statement of the final hemistich ἐπεὶ οὐδετέρῳ μέτα μηδέν has been related either to the affirmation that everything is full of light and darkness or else to the equality of the two forces (ἴσων …). The structure of the four lines and μετεῖναι have led to the adoption of the second solution. Indeed, the assertion in line 3, everything is full, is already shored up by a first causal statement, lines 1 and 2, so that the second assertion is very naturally related to that of equality. This is reason enough to set aside the translation “there is nothing that does not belong to one or the other of the two”; [34] moreover, μετεῖναι never expresses belonging to individual entities, but only to a group (“to be among”). When the argument turns back to equality, [35] one can understand either that the void is absent from each component, or that neither of the two forces impinges on the attribution of the other. Yet the expression τι μέτα [equivalent to μέτεστίν] τινι does not mean that one thing is included in another (see Karsten 1835:4: quoniam neutri inane inesti [“since the void belongs to neither”]), but that one thing participates in another (τινι μέτεστί means τινι μέτεστι τινος). Schwabl (1953, along with others) understands that neither of the two participates in Non-being (weil keine von beiden am Nichtseienden teil hat [“because no part of them contains the non-existent”]). [36] One does not see why Parmenides would have taken care to deny in advance the assimilation, which will be drawn from Aristotle, of Night to Non-being. On the contrary, he must have based equality on absolute purity and without any mixing of the opposed principles.

“In neither of the two [οὐδετέρῳ] is anything blended [μέτα μηδέν].” “Among” (or “in the midst of,” μέτα) has a strong predicative value (“nothing that is μετά”). [37] It will be understood, then, in accordance with lines 8.56–59, that neither of the two principles shares in anything—that is, in anything other than itself (Mullach 1857: quoniam neutri quidquam cum altero commune est [“since nothing of either is common with another”]; see ἑαυτῷ πάντοσε τὠυτόν, τῷ δ’ἑτερῳ μὴ τὠυτόν [“to itself everywhere the same, to the other not the same”] 8.57–58).

The unblended purity of the principles is maintained in the surprising geometry of their initial cosmic distribution. To interpret the fragments of the cosmology in the broad sense (10–15), we must not give up on Theophrastus’ interpretation, which is preserved in Aetius’s manual. Placed at the beginning of the chapter titled περὶ τάξεως κόσμου (On the Order of the Cosmos) (2.7.1), this text served as a referential framework for doxographic reflection on the spatial representation of systems. Theophrastus’ text can be divided into three parts. A first part summarizes a pre-cosmic or pre-cosmogonic structure; a second refers to the movements that give rise to the elementary differentiation and to the interaction of the principles; a third, finally, describes the arrangements of the parts of the world that has come into being, according to the title of Aetius’ chapter, “On the Organization of the Universe.” One stage follows from the other and leads to this end. To avoid the confusion that characterizes modern readings and compromises the rare attempts to rediscover the coherence of the whole, we must distinguish three developments in the text that correspond to different moments in the cosmographic construction. The first includes a purely geometric structure that is closely tied to the mutual exclusion of fragment 9.

Aetius (A 37) I: Before the cosmogonic movement

Preceding the concrete localization of the parts, at the center, at the periphery, and in the middle, the abstract schema presents in the first place the mode of distribution of the principles prior to any interpenetration:

A. The initial distribution (A 37 1 A)

Parmenides says that there are concentrically embedded spheres [stephanai] packed closely together, in each case one made of a sparse body and the other of a dense body; and others, blended, made of light and night, in the intervals between these.

The localizations τὸ περιέχον (“what surrounds”) … ὑφ’ ᾧ (“beneath which) … and τὸ μεσαίτατον (“the middle”) … περὶ ὅ (“around which”) … prove that we are dealing with spheres embedded concentrically and not rolled up or braided. [38] As for ἐπαλλήλους (“concentrically embedded”), the lexicon teaches us that the adjective does not designate alternation—which is expressed by τὴν μὲν … τὴν δὲ (“one … and the other”)—but rather close succession, without intervals. The existence of two pairs, one localized in the center and the other at the periphery, is explicitly mentioned. The immediate succession of fire and night at the two extremes shows that the mixed circles are situated in the interval maintained between the two pure pairs, the one in the center and the other at the periphery.

Figure 1. Diagram of the distribution of the spheres at the pre-cosmogonic stage.

The order in which the layers succeed one another from the absolute center to the absolute periphery—a dense layer, followed by a sparse layer, then by mixed layers, and finally again a sparse layer, followed by a dense layer that forms the outer limit—obviously does not correlate with the organization of the world that surrounds us [39] and that we see. The earth is not separated from the mixed zones of the atmosphere by a ring of pure fire. [40] If the speculative vigor of the system had been recognized, its self-evident pre-cosmic character would have been apparent; instead, the pieces of an incomplete puzzle have been permuted, always because of the rudimentary state of archaic science and the defective state of the information available.

The first part of Aetius A 37 preserves a symmetrical description that, as such, was not usable for a cosmography. This was the source of the difficulties. The symmetry appeared puerile and inadequate. No one, or almost no one, agreed to consider the schematic structure, and even those who did so retained its consequences only partially at best.

The decisive step proceeds, as is often the case, from an aporia; acceptance of the impasse leads to getting beyond it. If one opposes “mixed” to “pure” in the ordinary understanding and application of the terms, the orders are confused; the initial structure is assimilated to the later movements, which it determines. One is necessarily sent back to a “real” reference in the universe, either present or in the process of becoming, in a cosmogonic past. The problem of deciphering the figuration that is visualized but abstract is displaced, and it leads to endless discussions of attribution without an attributable object; it is de-intellectualized (“reified”). “Mixed” has to be understood with the idiomatic value of “mixed by virtue of the presence of the one and the other,” and thus “not mixed.” [41] For one pure layer, there would be, in the movement of division, two other antithetical layers of fire and night. On one, half of each; and so on. In this way, through a progression by division, the “mix” (interpenetration) is prepared; the separation remains complete, preserving antagonistic identities. [42] The dynamism of the abstract structure leads to the dynamics of the physical forces.

Theophrastus’ use of the word “mix” is not accidental, even if mixing as the rhythm of the partition is analyzed at the heart of the structure itself. It expresses the paradoxical truth of an organization that leads to blending through intensification of the antithesis.

If Theophrastus’ interpretation is correct by virtue of a deeper coherence than the mere possibility of solving the problems posed by the text, line 2 of fragment 12 does not describe a zone of blending, as it is commonly understood, but rather a closer and closer succession, which can be confirmed, on the one hand, with the help of the opposition with “pure” (ἀκρήτοιο, line 1)—there were layers of pure night before there were the layers of pure fire at the extremities—and, on the other hand, by the arrival at the median line, the place from which the goddess acts (line 3).

By reading Theophrastus’ text after Diels, with Parmenides’ fragment 12, and against Diels’ rather violent conclusions, [43] Reinhardt (1916) recognized that the first lines could not be related to the actual contemporary state of the world, but that they reproduced a construction that could not be assimilated to a descriptive system. [44] If he called this construction cosmogonic, it was in opposition to the cosmological or astrological explanation that had prevailed. In the second part of his book, he opted for genesis as opposed to system, and he accounted for what had preceded the genesis as the description of a previous or precursor state. In itself, this reading is neither true nor false, but in Reinhardt’s eyes it implied continuity and kinship, an implication that has led to (considerable) errors. The response remained determined by the position it was combating.

When the rings are interpreted as a stage in the cosmogony, as prior to a more decisive dynamism in the formation of the world properly speaking (which is assimilated to a koinè, extrapolated from the other pre-Socratics and thus explained by them), [45] the arrangement retained remains arbitrary. The arrangement, before it is upset, must have some signification with respect to the duality itself. [46] Meaning requires the arrangement of an alternation, and the pre-cosmogonic use of the stephanai.

If the blend is analyzed as a logical consequence of the doubled identity, [47] the maintenance of identity in the blend poses a problem. It is not self-evident. The negation of indistinct plurality takes place in duality. The structure of the rings means that the blend is produced by the negation, dominated and controlled by the autonomous principles (according to 8.55–59).

One cannot go back, before cosmology, to find the arrangement of the original duality, without also going back before the cosmogony. As a consequence, the pre-cosmogonic structure has to be—this is a postulate—closely related to the conditions and the beginning of the cosmogonic movements.

Fragment 12, lines 1–2

Contrary to what Fränkel had maintained, the first part of Theophrastus’ testimony is in perfect harmony with the data in Parmenides’ fragment 12. A system “as differentiated” [48] as that of Theophrastus may be more or less drawn from fragment 12. To be sure, this could not be done without the help of the summary.

The relation of the original fragments to the doxographic texts is different in each case. They can all be read thanks to Aetius; however, fragment 12 presents a part of the very process that is being summarized, whereas 10 and 11, which have a global and programmatic character, presuppose the completion of the system, in the coherence of its parts among themselves, as 14 and 15 do for the moon-sun relation. [49] The decoding is not the same.

Lines 1 and 2 describe the arrangement of the layers of fire and night, which, starting from the center and from the periphery, converge toward a line at the center of the mixed spheres. Lines 3 and 6 situate the goddess who presides over the blending in the most central of the mixed layers.

For the narrower ones are filled with fire without blending and the ones that follow are filled with night; further still the portion of flames shoots up.

The feminine forms αἱ … στεινότεραι and αἱ δ’ ἐπὶ ταῖς unquestionably refer to the spherical envelopes, called στεφάναι. The comparative narrower can be understood either as referring to the relative dimensions of the rays that separate the circles from the center or to the relative thickness of the layers. In the first case, the notion of “narrower” signifies “closer to the center,” and the succession is necessarily organized in a single direction starting from the periphery. [51] The progression is symmetrical: it starts, as A 37 confirms, from the two extreme limits. The second meaning is thus imposed: a thick layer of night is followed, in the direction of the periphery, by thinner fire, while the thick band of night at the periphery is followed, in the direction of the core, by a thinner band. [52] According to Theophrastus, the mixed circles are located in the interval between the two pairs. Scholars agree that the description of these circles is found in line 2, deeming either that, in a unidirectional progression, starting at the periphery, the mixed zone forms a third ring (or a series of rings) situated below the pure fire (after the rampart), [53] or else that, following the double progression, starting both from the center and from the periphery, the layers of pure fire and pure night are followed by mixed layers. [54] However, the “mix” in question here is not a simple blend. The plural αἱ δὲ (“the ones that follow”), maintained intentionally in Theophrastus’ paraphrase, indicates that the two zones of fire immediately adjacent to the core and the rampart at the periphery are both followed by a new band of night, which is in turn followed by fire.

Rather than understanding μετά as though the flame were shooting up in the middle of or in pursuit of darkness, or that it had been released (μεθίεται), [55] considered as a single mass extending over the entire median zone, it seems more accurate to put the adverb on the same level as ἐπὶ ταῖς, translating it as after, farther; the fire comes to place itself, in both directions, after the internal layers of night. With this reading, the mixed element would be actualized in the repetition without any blending of the two paradigmatic couples, which are doubled toward the interior. The term αἶσα, which says that the portion of flames is measured according to the law of distribution, signifies that the two layers of fire are added to the layers of darkness according to the same relation as in the external pairs.

The very reduced difference (which is acknowledged) inside a pair of contraries would not call into question the principle of equipollence, if the lesser surface occupied by fire, as compared to night, is compensated by the higher degree of intensity of one mass that is less inert than the other. The mobility and the relation between fine and dense matter would thus also be prefigured, at the heart of the initial division; difference in equality is its leading principle.

The text of the fragment does not indicate that the doubling of the pairs is pursued in the direction of the median line where the divinity of the blend resides, but the superlative in Theophrastus’ summary, the most median of the mixed elements, allows us to suppose that the initial structure is reproduced an indefinite number of times (see also the indeterminate expression μικτὰς δ’ ἄλλας) [“others mixed”]). Moreover, it is consistent with the logic of the system that in a first stage the two opposing forces occupy the whole without blending together. The term mixed, used by Theophrastus to designate the internal non-blended rings, is well explained by the hypothesis that posits a decreasing arrangement in which the interior pair, even while preserving the initial proportion of thicknesses, would consistently occupy the breadth of a single one (presumably the first) of the rings that form the preceding pair. The gradual shrinking of the intact rings prefigures and anticipates the interpenetration of the blending.

B. The extreme limits set by darkness (A 37 1 B)

What envelops them all, like a rampart, is solid, with an igneous ring below; and what is most central of all is solid, with another igneous ring around it.

Solidity is a property of night, as is density. It seems that one can infer from the pre-cosmic structure that the universe was circumscribed in an enclosure of two solid spheres (a full one at the center, a hollow one at the periphery). The use of the adjective “solid” (στερεόν) is thus distinctive; the consequence would be that this enclosure could be viewed as a stable part, surviving the upsetting of the geometry of crowns [56] and that, symmetrically, at the moment of this effacement the contiguous spheres of fire would be the privileged agents of the dynamism that is established, nourished at a distance starting from the median limit. The solid parts are obviously not assimilable to any of the elementary structures, as they are formed during the genesis, starting from the actual blending. The solid core will no more be the “earth” [57] than the external enclosure, designated by the analogy with a rampart. [58]

C. The middle (A 37 I C; frag. 12, 3-6)

The duality is canceled out at this breaking point in the system, where unification is sure to come about in the world between two contrary identities:

The sphere that is found in the absolute center of the mixed bodies is for all the “origin” and the “cause” [59] of the movement of becoming, a sphere that he names “divinity that governs,” and “that holds the parts,” [60] as well as Justice and Necessity. [61]

In the midst of these [narrower spheres] is located the divinity that governs all things; for everywhere it unleashes frightful engendering and union, leading the female to blend with the male and conversely again the male with the female (12.3–6).

A 37 interprets the eponyms of the anonymous power of blending, which governs (κυβερνῆτις) and which holds the parts, by the names Dikè and Anankè, [64] which appear in the doxa. As for the place this power occupies in the universe, it is incorrect to say, as everyone does, that Simplicius, disagreeing with us, situates it in the center of everything; he only replaces Parmenides’ terms ἐν δὲ μέσῳ τούτων by ἐν μέσῳ πάντων (Konstan 2014:34, 15). The error is explained by the fact that neo-Pythagorean speculation on the number and the place of the elements sometimes attributes to Parmenides, as it does to Empedocles, the theory of the central fire. [65] Defended by Zeller for the central localization, [66] the assimilation allowed Diels to shore up the conjectural inversion of the lower rings. In the first evocation of blending, the qualities of male and female represent the opposing forces. The symmetry of the movements, the female going toward the male and the male toward the female, illustrates that they initiate their strict equivalence even in union.

The place where the goddess is found is clearly defined. The localization is unproblematic provided that one understands the succession of rings as a complete symmetrical system traversing the universe without a break (since the genitive τούτων applies to the rings, ἐν μέσῳ necessarily refers to the median point). The structure of the pre-cosmogonic exclusion of circles situated closer and closer together produces blending, by pushing the division to the ultimate explosion, at the point where the circles meet.

Interpreted, the diagram would make it clear that union, in blending, results from division, thanks to the finer and finer demarcation of distinct entities. There would be a “blend” without blending, in the terms of the doxographic text, at the heart of the opposition. The two principles thus enter into the effective blend of the genesis of the world, while keeping their own identities; these identities are transferred and preserved beyond the dividing line. The relation between the initial abstract order and the dynamic phase of the constitution of the cosmic order becomes clear in light of this passage, which ensures the preservation of the inalienable features of each of the opposing principles, which are at once refractory and at the same time by that very token the authors of the blend. The goddess represents this law of duality constrained in the One; she presides over it and is produced by it.

All the other localizations that have been proposed, as products of conventional expectations, cannot be the results of analysis, since blending is presupposed to be present everywhere, before it has taken place. [67] The following hypotheses have been supported arbitrarily:

1. Of ubiquity. —If blending had already taken place (at the moment established by the line) and if it were therefore everywhere, one could judge that it was arbitrary to install the goddess of blending here rather than there. Thus Reinhardt and Fränkel—arbitrarily, it is true, for the meaning of the expression—analyzed ἐν μέσῳ as a “between,” μεταξύ (not “inside” but in the intervals between the rings). Since the rings were only partially blended, the universal principle [68] was limited to the places where blending prevailed, in the world (see Reinhardt 1916:12; Fränkel 1968:185: “Eine feste Lokalisierung ist mit diesem inmitten überhaupt nicht gegeben” [“No fixed location is given with this ‘in the middle’”]). [69]

2. Of the center. —Simplicius’ testimony (Konstan 2014, p. 34, 14–15)—“He represents the goddess installed at the center of everything, the cause of every form of becoming, as the efficient cause, one and common”—has been linked to the core, which for Diels is the central fire, [70] the Pythagoreans’ hearth (Ἑστία; D-K p. 242, ad frag. 12), whereas the reference is manifestly to line 3 of the fragment. [71] Guthrie, who like Gigon and others was looking for representations external to the system, assimilates the daimon to the Pythagoreans’ central fire, [72] here immersed in the chthonic depths, so that the eclecticism (or the “syncretism”) of the historian, projected onto the doxa, makes of the daimon Mother Earth and the dispenser of Justice, all at the same time. The tradition is an ancient one; Parmenides’ Pythagoreanism was common in the nineteenth century: “At the center of the universe the demiurgic divinity, generatrix of the gods and of all things, had her seat; one cannot but recognize the central fire, the creator mother god of the world of the Pythagoreans.” [73]

3. On the side of the periphery. —Berger (1895), in order to take the middle into account, chose the sun, among the celestial bodies, as the principle of life (in accordance with the solar cults). [75] For Gigon (1945:280–281), the divinity is transcendent; thus she dwells in the external igneous zone, beyond the rampart. The origin of the concept is situated in Xenophanes’ divine sphere, transferred by Parmenides into “the world of general opinion.” This would be the true god, representative of Being; the goddess in fragment 12, comparable to Aphrodite (frag. 12.4–6; see the authors cited and combated in Zeller-Nestle 1920:171n1) in the lunar region of men, would be a secondary force, originating in the other, delegated “into the blend” (the middle is only one “region” for the true god). The indications pertaining to the union of the sexes at the end of the fragment are used in a restrictive way.

Some scholars accepted that at least for Theophrastus, if not in reality, the goddess was “where night and fire blend.” [76] Reduced to this observation, the assertion is almost meaningless.

Reinhardt’s position, contradictory only in its impure application, was clearly anticipated by Karsten and others (Reinhardt was situating himself vis-à-vis the scientific authority of his immediate predecessors and did not look further back): habitare hanc Deam … paribus intervallis a mundi centro et circuitu distantem, unde ipsa … moderator (“The goddess lives … at equal distances from the center of the universe and at a distance from the circuit … of which she is herself the ruler”) (Reinhardt 1916:252). The research could have been linked to that of Karsten and the others, as was the case nearly a century later, in Nestle’s conclusions at the end of his discussion (Zeller-Nestle 1920:718).

Cicero’s testimony in De natura deorum 1.1.28 (28 A 37) is easily harmonized with Aetius’s account if we recognize that the term “crown” is transferred to one of the five parts of the ordered world, the ether below the firmament. [77] This zone may be said to be filled with fire or with light, and may be said to “encircle” (cingit) the sky, namely, the median zone that Parmenides calls god. As this zone is indeed the substitute, after the cosmogony, of the point of origin of the blending (according to A 37 and B 12), the assimilation is not illegitimate. The murky light of the Milky Way is the sign of blending. The presentation followed in the doxographic account “on the god” in Cicero, with “crown” in the singular, suggests that a theological transposition has interpreted the ethereal zone two as a halo around the head of “the god.” The daimon has as its finery this stephanè (wreath). The association between the wreath and this beyond-the-sky, which is seen as the god’s extension, is not accidental.

Aetius (A 37) II: The cosmogony, the dynamism of fire

Since the geometric structure of the rings cannot be identified with a phase of the genesis of the world, the cosmogony is organized around its eradication, in blending. As it propagates itself, blending produces the new delimitations that coincide with the major zones of the universe. Theophrastus, in the second part of his summary, clearly marked the principal events:

And the air formed upon leaving the earth, rising in vapor owing to its more violent compression; as for the sun and the Milky Way, they were formed by the breath escaping from the fire. The moon is a blend of the two, both air and fire.

Like the succession of alternating spheres, the cosmogonic movements start both from the center and from the periphery. But a dissymmetry appears at once. The centrifugal movement that starts from the “earth,” from the central core, occupied by night, is triggered by the whirlwinds of fire. The centripetal movement develops, starting from the fire that has collected under the solid vault. The reason for this dissymmetry is that, in a first phase of the blending, fire had risen up from everywhere, crossing the barrier set up by the dark rings; concomitantly, night established itself below. The intensification of the blending, indicated by the comparative more violent compression (βιαιοτέραν … πίλησιν), reverses the movements. Under the influence of the rotations of the fire, night rises, in the form of air; the fire spreads and descends to form the sun and the Milky Way. The moon is born following the meeting of the two convergent emanations of air and astral fire.

The upheaval that results from the blending is so total within the enclosure that one cannot infer the orientation of the movements of localization of the two principles within the delimited space. [78] The structure produces the blending. The distribution was at the origin of a potential movement, first paradoxically logical and static, leading to the dynamics of the blending. The physical world grew out of the confrontation of contraries “without blending.” Once the upheaval has taken place, the structure is entirely abolished, which amounts to saying that the powers are acting, in the intermingling, according to their own antithetical attributes. Fire will then, according to its own property (κατὰ … δυνάμεις, frag. 9.2), be more mobile, more “efficient” in the categories of the Peripatetics.

In deciphering the pre-cosmogonic structure, according to its own logic, one recognizes that the blending produced by the increasingly weak opposition, by virtue of the thinness of the layers, takes place in the middle, at the equidistant point, but that the force is all the greater, since the pure masses were more extensive at the two extremities, so that the parts of the fire, by coming back together, freed themselves and precipitated the decantation of the heavy principle. The ascendant movement asserts itself; it bends to circularity through the roundness of the form at the extreme ends of the initial distribution of the layers. The increased compression of the fire leads at the center to the expulsion of the intermediary “elements” (water and air); it presupposes a violent, swirling action of the fire, of which the orbits of the astral bodies will be the regularized residue. [79] The global form of the structure determines the form of the movement, and thus the circularity of the bodies that it fashions; by the same token, the roundness of the earth is not posited as an initial given but results from a series of processes in keeping with the dynamism imposed by the framework.

The earth is constituted when density, in response to the rising movement, is precipitated toward the center. [80] If we take another doxographic testimony literally, some “air,” becoming detached from the fire, was then compressed to the point of giving birth, in a first phase, to the hard bodies of the earth, before the expulsion, at a later stage, of water and vapor [81] (a first form of air, ante, then a second, post, escaping under the influence of the celestial rotations).

Figure 2. Arrangement of the parts of the world.

If the moon is made of air and if fire (according to A 37) is formed from one of the blends (the cold) from the median zone (A 43), the air in question might not be the air that was separated from the earth (τῆς μὲν γῆς ἀπόκρισιν), but rather the more primitive representative of night, captured in the center, in the Milky Way. Two different blends oppose one another in the sun and the moon (according to A 43).

The program of fragment 11

The information supplied by the doxographer is corroborated by the only fragment of the cosmogony, preserved in Simplicius’ commentary on Aristotle’s On the Heavens (Comm. Arist. Gr. [82] VII, 559, 22–25):

How the earth, the sun and the moon, with the common ether, with the Milky Way, the outermost Olympus and the burning force of the astral bodies entered into their becoming.

This fragment has been neglected. Mansfeld, for example, does not consider it; Gigon sets it aside. [83] Hölscher makes no comment. [84] Von Stein had declared that the lines were not authentic. [85] Deichgräber (1959) for his part preferred to attribute them to another author; he thought of Empedocles [86] because of certain words found in the fragment.

Beyond the formal testimony of the citation (they, that is Parmenides and Melissos, speak clearly of a birth of perceptible things, Comm. Arist. Gr. VII, 559, 19), the verbal group ὡρμήθησαν γίγνεσθαι, which adds the inchoative aspect to the duration of becoming (Simplicius presents the citation in these terms: Parmenides says that he is beginning to speak of perceptible things, Comm. Arist. Gr. 20–21), proves that in these lines we have the beginning of the stage in which the formation of the parts of the world was described. The program announced was exhaustive. Between the earth at the center and the vault, called external Olympus (ὄλυμπος ἔσχατος), with which the fixed stars are closely associated, the sun and moon are situated, forming a pair, then the ether, called common (ξυνός), and the Milky Way, called Uranian (οὐράνιον). An account in Aetius (II.20.8 a = 28 A 43) establishes, by specifying the indications given in A 37, that the sun and the moon did not emerge directly from the fire that descends and the air that rises, but that they were separated from the Milky Way, the sun from the thinner blend, which is hot, the moon from the denser blend, which is cold. In fact, the Milky Way is not an emanation of the fire, but, as we learn from another account (III.1.4 = 28 A 43 a), it is nothing other than the blend formed by the meeting of the two emanations. According to a third account, in the chapter on the order of the celestial bodies (III.15.4 = 28 A 40 a), the sun, coming after the other planes, is situated below Venus, [87] just above the Milky Way, which the doxographer calls the igneous zone and Parmenides calls “heaven,” οὐρανός (see the epithet οὐράνιον in 11.2). The moon, a relatively cold blend, receives its light from the sun (Aetius II.26.2; II.28.5 = A 42), and turns out to be placed just below the median zone. This arrangement is in harmony with the function of the ether as revealed by the epithet common, which takes its meaning from the power held by the layer of pure fire, separating Olympus from the Milky Way, to cross the median blend and to inundate with light, when the resistance is not too strong, the lower region of the atmosphere (ἀήρ). As the moon receives its brightness from the sun, the terrestrial region is lighted during the day by the common ether.

The traditional interpretation understands as “common” the circular envelopment of the world by the diffuse ether. Untersteiner applies the idea to the duality of day and night; at the outer edges of the sky (namely, the firmament), the ether embraces the (internal) temporality and the atemporality of Being (1958:CXCIIIn98). The communication that is established by the ether in fact connects, intra muros, the separate parts of the world. The division is achieved, and is thus surmounted, in the ether.

The communication proceeds in ascending order, but without a simple succession. The elements regroup. After the earth (5), come the astral bodies that concern it directly (2 and 4). They are situated symmetrically on one side and the other, above and below the heavens with the Milky Way (3). The ether of the upper zone (2) is “common” because it connects Olympus to the atmosphere; its light crosses the sky below to penetrate all the way into the lower zone of the moon. The sun (in the ether, 2) and the moon (4) surround the median zone (3), The Milky Way (3) and Olympus at the extreme point (ἔσχατος) (1) surround the ether in turn; it is thus named in relation, mediated by the sun and the moon, with the earth; then situated between the astral zones below and above. [88] The enclosure of the whole is marked by the extreme limits at the beginning and the end (the earth and Olympus, 1 and 5).

The fixed astral bodies are distinguished as an entity of the vault, Olympus. Heat is not exclusive to the sun that heats the earth. The other astral bodies, originating from the same principle, have the same property, which escapes us. It is not transmitted to us. Whereas the sun and the moon, originating from the median blend, attest by their difference to the opposition of thin-hot and dense-cold, the astral bodies of the vault, originating at the outer limits of pure fire, are hot (hence their distinctive epithet, “burning force” (θερμὸν μένος), in relation to the localization at the extremities: “outermost” (ἔσχατος).

Aetius (A 37) III: Beyond cosmogony, the division of the world

The third and properly cosmogonic part of Theophrastus’ summary confirms the analysis of the cosmogonic process.

As the ether extends in circular fashion in the highest region of all, the igneous zone, the very zone we have called the Heavens, is placed below the ether, and below the Heavens, in turn, the terrestrial region is placed. [89]

It is essential not to confuse the ether, the region of pure fire, with the solid nocturnal envelope, the zone of fixed bodies, which Parmenides calls Olympus. [90] It is no less essential to recognize that Theophrastus astutely emphasizes, precisely because the thing is astonishing, that the intermediate zone of the Milky Way, included between the ether and the περίγεια (“the terrestrial region”) is given the name Heavens (οὐρανός), following the Parmenidean use of the word that is found in fragment 11 (οὐράνιον). One must not be led astray by the term “igneous” (πυρῶδες); it designates the Milky Way. In fact, the blend is characterized this way because of the stars that shine there, entities that must not be confused with the fixed bodies (see Aetius II.15.4 = A 40 a): τοὺς ἐν τῷ πυρώδει ἀστέρας, ὅπερ Οὐρανὸν καλεῖ (“the stars in the fiery region, which he calls heaven”); the mood is characterized as igneous like the sun (II.25.3 = A 41), its blend is cold, and its light is borrowed (see fragments 14 and 15). If a final proof were necessary, we have the passage in Cicero’s De natura deorum, in which a ring of light—that is, ether—encircles the heavens. [91] When one fails to identify the heavens with the blended zone of the Milky Way, one does not understand why it is called god, and described as the origin of births, in conformity with lines 3–6 of fragment 12 (the masculine deus for δαίμων is explained by the syntactic agreement: caelum, quem appelat deum (“heaven, which he calls god”); the absence of identity is expressly asserted: in quo neque figuram divinam … suspicari potest (“in which no divine form … can be supposed”): the divinity is nameless. [92]

All that men see of the sky, taken as the reunion of the astral signs, is perceived in relation to the assembly of the milky trail in the center, and, as it were, through that trail. Thus Parmenides distinguished the igneous zone “which we have called [κεκλήκαμεν] the Heavens,” from the reference points that are above the planets in the ether and the fixed bodies in the firmament (called “Olympus”).

Fragment 10. —The lines of fragment 10 sketch in the cosmology, the current state of the world; they expose the internal tripartition that is reproduced by Theophrastus:

—the upper region of ether with Hesperus for the planets, up to the sun:

you shall know the birth of the ether, all the signs that are in the ether, and the always clear works of the pure torch of the very brilliant sun, as also the place from which they emerged to be born;

—the lower region of terrestrial air with the moon:

ἔργα τε κύκλωπος πεύσῃ περίφοιτα σελήνηςκαὶ φύσιν,

you shall also learn the vagabond works of the round eye of the moon as well as its birth;

finally, the intermediate region of the galactic blend called the sky:

you shall know the skies, which maintain apart, on both sides, the place from which it is born, and how, leading it, Necessity stopped it to hold the limits of the astral bodies.

It suffices to give ἀμφις ἔχειν the (epic) meaning of to separate on both sides in order to be constrained once again to give up identifying the sky with the external limit of the world (περιέχον). Interposed between the ethereal region and the vaporous region, the Milky Way is the place where the divinity who governs acts. It is she who, under the name of Necessity (see A 37), leads the expansion of the blend, on both sides of the median line, and stops the course of the astral bodies, preventing the sun from penetrating into the atmosphere and the moon from rising into the ether.

While the arrangement of the proem of fragment 11 corresponds to a very erudite entanglement, from which one cannot directly infer an ordering, that of fragment 10—which, on the contrary, corresponds to an ordering (2 4 3: extreme terms, middle) [93] —serves as testimony rather than as proof, although the triad (ether-sun, then moon, and the sky between the two), is a configuration attested elsewhere in Aetius. [94] The lines presuppose not only something that follows, regarding the center of the universe, but also a preceding part, which is missing, on the bodies of the periphery. Fragment 10 is constructed differently from fragment 11; it does not serve a dual purpose. The affinities of composition with the end of the proem (frag. 1), and also the affinities of structure (see μαθήσεαι, 1.31; εἴση, εἰδήσεις 10.1 and 5), suggest that the lines come from the part of the proem that came immediately after 1.32. [95] The cosmology would thus be anticipated in the announcement of the content by the daimon. Archaic thought is said to know a thing by knowing its origin, its physis (the primitive is an aspect of primitivism). [96] The “origin” marks rather the supremacy of the interpretation over the things themselves; the prior elucidation of their formation makes it possible to say what they truly are, or what one has to acknowledge that they are in order for them to be understood.

Instead of recognizing in the participle ἀμφὶς ἔχοντα a reminder of the encompassing function of what was taken for an envelope surrounding the world (“the all-embracing sky”), [97] Untersteiner, who saw the time of the astral bodies separated at the outer limits of the atemporality of the ἐόν (“being”), proposed the translation “che da una parte e dell’altra [ἀμφίς] allontana” (“separates on both sides”), following the Homeric usage of the figure (1958:cxcii and n94); the function of division fell back on what was, for him, conflated in a unity, οὐρανός—ὄλυμπος—αἰθήρ (Ouranos—Olympos—Aither). He would have had to tell himself that all that could or should be distinct. But the separation, provided that it is transferred to the median zone of the sky, offers a homology that can be maintained.

Anankè is at the outer limits of the world because it is situated in the heavens, as is written in fragment 10 (line 5), and because the heavens are naturally associated with Olympus; [98] yet the texts distinguish between the two: Aetius (A 37, but also A 40 a, 43 a) situates the heavens after the igneous zone of the ether with the planets, which is below Olympus (the vault); Parmenides himself, in fragment 11, clearly dissociates the Milky Way from the sky (γάλα τ’ οὐράνιον), between moon and sun, and from Olympus at the outer limits with the fixed bodies. The commentators have thus found in Necessity a force that encloses [99] and holds together, starting from an extreme limit. The logic of the system, which the common expectation must experience as a paradox, would have it on the contrary that it holds together starting from a median limit, by means of a separation so perfectly “right” and balanced that it has its principle in the point of encounter. Necessity thus lies in the equipollence produced by the duality of the distinct principles.

The system of astral bodies is governed and regulated from the center of the world. The difference in viewpoints is fully apparent in the translation of the ἀμφὶς ἔχοντα of fragment 10, which, in the logic of the general distribution determining the median separation of the celestial zone, must be understood as “setting aside” toward the upper and lower regions, whereas the common representation leads to the repeated reuse of a translation “encircling all around,” which is in contradiction with the structure of opposition.

Parmenides’ cosmology has incited far fewer studies than the ontology on which it is based. For a long time, it was not attributed to him. What makes the interpretation of the physical system so arduous is not that there are gaps in our information, however real these may be, but the force of abstraction in the representation of the world, which is just as strong as the force of speculation in the definition of what is. Rigor makes the reconstruction easier, allowing us to rely on the implacable logic of the whole.

Originating in the contrary tensions that traverse the figure of visualized Being, the opposition between the elementary powers is reaffirmed at the various stages of the perceptible revelation. The initial, geometric diagram of concentric circles makes comprehensible the description of the cosmogonic process leading to the rise of fire and the descent of the dense element. The blend resulting from the median encounter produces new separations. The cosmology makes visible the primordial antagonism in the regions of the universe, the ether lodged under the nocturnal vault, the atmosphere surrounding the terrestrial globe, and in the middle the divine region, called the sky or the Heavens, of the differentiated blends and of separation. The gentle (ἤπιον) light of perceptible knowledge, where Aristotle saw an equivalence of Being, is spread over the ordered totality of phenomena, over fire and what is not fire, and ends up harmonizing with knowledge because it is regulated according to the figuration of Being.

[ back ] 1. That other study and debate remain open, however. On the subject of sphericity as a decisive stage in the progression, see Bollack and Wismann 1974 on verses 42–49 of fragment 8 (D-K numbering).

[ back ] 4. Burkert 1962:286n45: “In general, it is regarded as an almost hopeless task [the preliminary is at the origin of the failure] to reconstruct the celestial system of Parmenides” (cited from Burkert 1972:307n40).

[ back ] 5. See below, p. 200. There is a definite relation between the incoherence and the eclecticism of the borrowing. The objective restorations are entangled in the muddled nature of the material.

[ back ] 6. One can go further back, as Morrison does (1955:6), relying on Homer and Hesiod, and find a double system of hemispheres, above and below the earth, which is at the center, without this center being the “center” of the goddess. Guthrie’s irony reinforces the discredit heaped on the topic (Guthrie 1965).

[ back ] 7. Guthrie 1965:5–6: “… suppose that Parmenides is doing his best”: “I can at least help you to understand it better than other people.”

[ back ] 8. See Mansfeld 1964:164; note 1 contradicts the assertion in the text.

[ back ] 9. See the same guiding principle in Finkelberg 1986; see also below, notes 38, 39, and 42.

[ back ] 10. See the ring of fire circling the earth, Tarán 1965:234–237; see also below, pp. 186–187.

[ back ] 11. See, for example, McDiarmid 1953. The fictitious Aetius cannot be mistaken for a Theophrastian; he is too visibly contaminated by Stoicism. There is no way to localize the goddess.

[ back ] 16. In place of στερεόν περὶ ὃ (Boeckh, but without στερεόν, for περὶ ὃν F, περὶ ὧν P) πάλιν πυρώδης (scil. στεφάνη), Diels had put the following in his text: στερεόν, <ὑφ’ ᾧ> …

[ back ] 17. See Burkert’s critique (1962:296, and n. 115; in English, see Burkert 1972:317, and n. 92).

[ back ] 18. The modifications ended up remodeling the text of A 37. Among the earliest were those of Susemihl 1899 and Döring 1911; see Zeller and Nestle 1920:71, n. o.

[ back ] 19. “Parmenidesstudien” (1930), in Fränkel 1968:157–197. The outline has frequently been adopted by others. “Parmenidesstudien” can be found rev. and trans. as “Studies in Parmenides,” in R. E. Allen and D. J. Furley, eds., Studies in Presocratic Philosophy, vol. 2: The Eleatics and Pluralists, 1–47. London, 1975.

[ back ] 25. It is a matter of the whole, or a part, ad libitum. For Fränkel (1968:183n1), the “crowns” designate both the circles of the stars (Sternbahnen) and the spheric envelopes (Kugelschalen). Gigon (1945:279) has a contrary opinion: “They naturally cannot be considered as rings,” on the same basis as the circuits of the celestial bodies.

[ back ] 26. See the void between the moon and the earth in Fränkel 1968:185 and Fränkel 1951:413. The moon is for “the world of men,” who aspire to evade their nocturnal prison.

[ back ] 27. The alternation of the rings had been introduced by Theophrastus following an erroneous interpretation of frag. 12.2 s. He had made the role of fire (μετά) autonomous in the circles of darkness (Fränkel 1968:183).

[ back ] 28. The translation “in alternation, the one formed of … the other of …” (Fränkel 1968:183) is not the correct analysis of ἐπαλλήλους.

[ back ] 29. στεινότεραι is applied to the purest celestial spheres, and μετά is read as an indication of the blending that has already taken place.

[ back ] 30. Untersteiner 1958:cxciv: “This astral cosmology, which is particularly well developed among the Eleatics—in a much more systematic way than among the other pre-Socratics—has a precise raison d’être” (the relation of the celestial bodies among themselves, creatures of time …).

[ back ] 31. See the scholia ad 8.59: “… by names in conformity with their powers” (Couloubaritsis does not account for καὶ τὰ κατὰ δυνάµεις, for the difference between light and darkness or for the properties of the two “powers”). A double nomination, global and particular.

[ back ] 32. To the contrary, Coxon (1986:84) and O’Brien (1987:61), follow Diels-Kranz (and see Karsten 1835, earlier) to link the group ἐπὶ τοις … with ὀνόμασται (see also Tarán 1965:161, with a different construction of τά: “and these …”); Mansfeld (1964:148n3, 149) is even more acrobatic, as he connects the prepositional complement to the multitude of the particular (“ihrer jewelligen Einzelstruktur … gemäss benannt” [“named in accord with its jewel-like single structure”]). Plenitude (πλέον) results from a totalization of the capacities by an extensive power of two principles: δυνάµεις ἐπὶ … . These are properties of Night and Day; their differences are revealed in the multitude of things.

[ back ] 34. Thus Fränkel 1968:181, adopted by Kranz (“was unter keinem von beidem steht” [“what pertains to neither of the two”]), as opposed to Diels; then Calogero 1977:52n47; Verdenius 1942:77 (“… that does not belong to either”); Tarán 1965:164; Guthrie 1965:57, and so on. More recently still, Cordero 1984:40 (more concisely, “for outside of it there is nothing”); the translation of the preceding line, “What has its proper powers has been named grace for these or for those,” is difficult to analyze. What are the referents?

[ back ] 36. See Schwabl 1953:64; for the same analysis, one can cite (among the most recent authors) Mourelatos 1970:85: “since nothingness partakes in neither”) (relating the explanation to πλέον); Couloubaritsis (“does not harmonize [=?] with nothingness”), and so on; see also Mansfeld 1964:150–153.

[ back ] 37. The subject of the subordinate clause (μηδέν) names the element of the mix that is excluded, as a rejected possibility. Mansfeld’s translation (1964:156), “weil keines von beiden Anteil hat an Nichts” (“because neither of them has to share anything”) could (except for the capital letter) be justified, against the hypostasis of nothingness or Non-being (“neither of the two contains a nothingness” [Hölscher 1968:107; “a …” ?]), which substitutes a judgment of existence (Hölscher: “of reality”) for the definition of the reciprocal relation of exclusion and purity. O’Brien (1967) makes the task extremely difficult by supposing that the rigorous separation between the two principles implies the (denied) possibility of a matter that is not used. He thus makes οὐδετέρῳ μέτα the subject of the clause “what is not part either of the one or of the other” (οὐδετέρῳ μέτα, without a participle), and he makes μηδέν a judgment of existence (“is nothing”). One cannot say that this sentence contains a double negative (p. 62); for O’Brien, the subject is determined negatively. There is no doubt that the analysis of the noun phrase requires the predicative value of μέτα (grammatically μέτεστιν): nothing is a part … . See also Owens 1974:391; he takes μέτα to be an adverb: “for neither can there be sharing in any way at all” (see also n. 30).

[ back ] 38. As some have understood. For Finkelberg (1986:312n24), the term “braided” is chosen by the doxographer because it translates the actual mix; it does not apply to the pure spheres.

[ back ] 39. Finkelberg, in contrast, reads the first part of A 37 in such a way as to establish a correspondence, as has always been done, between the “rings” and real referents in the contemporary world. Thus for him the mixed rings are not inserted between pure pairs: there is no darkness in the heavens, but a mix only below the ether; at the center, fire is localized under the terrestrial crust, following the ancient opinion (see Zeller, Diels, and so on); and see below, p. 108.

After the mention of the solids in Aetius (in the center and at the periphery—my 1b), his reading, in a dissymmetry that is more cosmographic than Parmenidean, arrives at a pair (fire/darkness) in the center, around the core, for which there is no corresponding pair at the periphery, under the rampart (fire/mixed). The dissociation is arbitrary.

[ back ] 41. Which does not prevent the use of “mixed” for the stage of actual interpenetration (frag. 12.4).

[ back ] 42. Finkelberg raises questions (understandably) about the difference that would make it possible to distinguish each unit in the series of mixed, contiguous rings (pp. 209–210). There is, as for others (see above), only a single region of the world. The question, which ought to have been maintained, was not compatible with the prejudice in favor of the immediate cosmic reference. Finkelberg’s interpretation of 12.1–2 (1986:309–312) cannot be defended; there is no darkness that follows the mixed layers; for him, lines 1–2 are divided between a fire, c (in the center) darkness, b (in the third place, μέτα) mixed. He reserves the mixed layers for everything that is intermediary between earth and ether.

[ back ] 44. Reinhardt (1916:11) was deciding among three hypotheses, the spheres of this world (1), according to the positivist interpretation offered by Diels or Burnet (1930), an order preceding the one that results from the formation of the world (2), or the symbolic expression of the system of physical laws (3). The third is hard to distinguish from the first; in fact, they merge.

[ back ] 45. In Hölscher’s attempt (1969:109), relying on Empedocles (A 49 = 174 Bollack 1972) for the cosmogonic connection, following Reinhardt, the comparison with the later systems introduces a more structural element, in contrast to the dependencies always taken up again by the “Pythagoreans” or by Anaximander.

[ back ] 46. See Hölscher 1969:108: “permitting the passage from the pure duality of the contraries to the cosmogony.” Distributing the rings of fire around a center, and—toward the periphery—around the rings of darkness, Hölscher has, except for the center, a separation of the two masses, but neither their relative separation nor the rings or spheres take on any meaning here (he reserves them for the divisions that result from the cosmogony, and thus in fact for the astronomical spheres as well, as the constructions that are being combated).

[ back ] 47. As Hölscher (1968:25) formulates it in Anfängliches Fragen, following Reinhardt (Reinhardt 1916:74ff.; see also Hölscher 1969:198ff).

[ back ] 48. See Hölscher 1969:107ff. He writes that the text (A 37) becomes even more disconcerting if it is confronted with B 12.

[ back ] 49. O’Brien does not consider A 37 (1967:17 ad 12.1–3). The arrangement that he proposes (247) suffers from this lack. The specificity of fragment 12 does not appear; the announcement of the cosmogony (frag. 11) probably is not linked to an earlier stage (see Bicknell’s [1968] hypothesis concerning Parmenides frag. 10; and see below, p. 209. In any case, one cannot conclude from the “works” (of the sun and the moon) that it is a matter of a later “development.” The two aspects, the origin and the effects, are definitional, complementary, and general.

[ back ] 52. The word “for” (γάρ, 12.1), abrupt in the quote from Simplicius, may relate to the exclusive distribution. The purity of the external spheres of darkness is symmetrically related to the purity of the internal spheres of fire. The decision to translate στεινότεραι by “nearest” (to the median line of encounter) rather than “narrowest” is understandable (Reinhardt 1916:13), but it is problematic.

[ back ] 53. See Fränkel 1968:184, according to a principle of progressive decrease in light.

[ back ] 54. See Zeller-Nestle 1920:701, where the symmetry is preserved (provoking the correction by Diels that has been discussed).

[ back ] 57. The assimilation is constant: see Fränkel 1968:184: “der Weltkern (die Erde)” (“the world-core, the Earth”). The distinction is made clearly by Finkelberg (1986:307), but, as he maintains the idea of a fire in the interior of the earth (on the model of Etna or Vesuvius), the core will be solid and yet distinct from the earth (a b a). He constructs, in disagreement with frag. 9 and (many) other testimonies, a third space of bodies, which would be what is called the “solid” (see p. 304).

[ back ] 58. Seeking equilibrium in the current situation of the world, where the heavy and the murky are localized in the center, Gigon concludes that all the fire must be located at the periphery. A shell of fire then surrounds the ether and the igneous sky (1945:279). The aporia did not escape him, but the “realistic” and anti-constructionist bias prevented him from re-evaluating his hypothesis. Better to remain with the aporia (even if it were absurd). Later on (280), he imagines a wall (of ice?) separating the divine fire from the empyrean realm of the ether.

[ back ] 59. The text has a gap after ἁπάσις. Only τε καὶ can be read; Diels completed it with <ἀρχήν>, following Simplicius, On Aristotle’s Physics (cf. ad B 12): πάσης γενέσεως αἰτιάν, which does not pose a problem for the basic content. One may prefer the cruces, as Coxon does.

[ back ] 60. The transmitted term κληροῦχον is ordinarily corrected as κληδοῦχον (Fülleborn 1795, in keeping with the proem, frag. 1.14). The grouping is problematic. If Δίκη and Ἀνάγκη are taken together, as a thing (see τε καὶ), κληροῦχον could be an epithet for this group. According to the other option, the adjective also qualifies δαίμονα, and the two nouns are in apposition.

[ back ] 61. The organization of the divine powers (theology) and anthropology are not included in this study, however linked they may be to the analysis of the cosmic structures.

[ back ] 67. Zeller’s reasoning (Zeller-Nestle 1920:717n1d) has its logic, in a non-egalitarian dualist vision, which is not that of Parmenides: if the blending is to the benefit of corruption, Aetius’ text cannot have placed the goddess in the center of the less perfect spheres.

[ back ] 68. “Omnipresence,” according to Mansfeld (1964:164). Rightly so, but on the basis of a single instance (and an instant), and without limits.

[ back ] 69. “… everywhere the antagonistic principles are in contact,” the goddess is at work. For this opinion, one can cite Verdenius 1942:6 and n. 4; Mansfeld 1964:164. Reinhardt (1916:13) had delimited the equidistant point, but since he recognized a blend actually achieved on both sides, the interpretation—which was in fact correct—was contradicted by Reinhardt himself.

[ back ] 70. Aut coronarum omnium (“either of all the crowns”), according to Theophrastus, A 37 (Fortenbaugh and Gutas 2010), the region of the sun (for purity; for Gigon, it will be the moon, on the side of corruption); or else “the center of the universe,” aut universi (“or of the universe”), according to Simplicius. The interpretation is an ancient one: see Karsten (1835:251ff.): Plerique ita intellexerunt … . Sic Simplicius (“This did many think … so Simplicius”). (Parmenides used the Pythagorean central fire, but had to substitute the earth for it). Neither Reinhardt (1916:12) nor Fränkel (1968:185) doubted this central localization, attributed to Simplicius. Like Theophrastus (Krische apud Zeller-Nestle 1920:717), Simplicius could have been mistaken about the meaning of 12.3. Karsten himself (1835:252), however, had positioned himself on the side of the median line, according to Stobaeus (paribus intervallis a mundi centro et circuitu distantem, “distant by equal intervals from the center and circuit of the world”), against Simplicius, on the interpretation that he (Karsten) never renounced. Finkelberg, finally, interprets fragment 12 according to Simplicius’ erroneous but accepted meaning, and proposes to correct Aetius in order to achieve consensus (1986:311 and n. 21).

[ back ] 71. The uncertainty, “going back to Antiquity” (Hölscher 1969:108), stems from this Dielsean interpretation of Simplicius.

[ back ] 72. “This, to his probably Pythagorean-trained mind, was the daimon …” (Guthrie 1965:64).

[ back ] 74. See also Tannery, taking the doxa to be a Pythagorean doxography that was polemical in character (1930:236); and Tannery 1884:285: the divinity is “at the center of the universe”; Tannery took the crowns to be nested cylinders. The position of Burnet (1930:169–196), who believed that in the doxa Parmenides was exposing a doctrine that he had gone beyond and that his disciples must have known, the better to combat it, remains dependent on the a priori of that tradition (see, once again, Guthrie, after Cornford, and Raven, and the metamorphoses of Pythagoreanism; Burnet is still following Pythagoras and the oral tradition, although sometimes this position is mitigated by Ionian speculations). Against the Pythagorean assimilation, Anaximander is placed in the forefront by Burkert (1962:261n31; in English, see Burkert 1972: n25).

[ back ] 76. Hölscher 1969:108. For Deichgräber (1959:66), the goddess comes from before the blending (see frag. 12); she is thus inherent to the principles, outside of the blend. What was her function there?

[ back ] 77. When the heavens are associated with the Olympus of the fixed bodies, the igneous zone must be situated beyond the extreme limit, as a materialized transcendence, an empyrean beyond the limit: “Das erste ist ein Feuerring um den Himmel herum [Gigon was thinking about the fixed elements]. Diesen Ring nennt Parmenides Gott” (“The first is a ring of fire around the sky. Parmenides called this ring God” [1945:280]). The ring of fire is “the representative of Being, whereas the earth is the representative of Non-being” (one might add sic).

[ back ] 78. As Hölscher does, supposing that the rings of fire, around a center, were embedded below the rings of darkness, so that in the cosmogony fire rises upward (1969:108).

[ back ] 79. See the force, the thermodynamics of the fixed bodies, θερμὸν μένος, frag. 11.3.

[ back ] 80. In the doxa of the Stromateis, 5 (Doxographi, p. 580 = 28 A 22), λέγει δὲ τὴν γῆν τοῦ πυκνοῦ καππυέντος ἀέρος γεγονέναι, ἀέρος was eliminated by Patin (1889:625), then by Diels, and so on; it was defended by others who saw in air a designation of darkness, without contradicting the origin of the atmospheric air by a later compression, according to A 37 (see the references, including those of Burnet and Gigon, listed in Untersteiner 1958:20ff., ad A 22 in fine). It is then necessary, notwithstanding the order of the words (τοῦ πυκνοῦ καταρρυέντος ἀέρος), to translate as “when the dense air was precipitated downward.”

[ back ] 81. The epithet for the earth, ὑδατόριζον (B 15 a), might, in density, be aimed at the aquatic origin of the earth by designating the solidifying mud (and might then be applied from this angle to existing geographic representations, such as the Ocean, which rolls itself up; see Untersteiner’s doxography, ad l).

[ back ] 86. Possible confusion on Simplicius’ part, p. 64n1. Conversely, Stein, despite the very characteristic style, had attributed frag. 10 to Empedocles, in order to eliminate the problem.

[ back ] 87. The shepherds’ star, identified with the morning star (see also Diogenes Laertes’ “Life of Pythagoras,” 9.23 = A1; 7.14); see Burkert 1962:285 and n. 43 (Burkert 1972:307 and n. 39). We do not know whether other planets were named; if not, Hesperus corresponds to a choice.

[ back ] 88. The common representation of the interpreters groups the ether, the Milky Way, Olympus, and the fixed astral bodies according to the realistic preliminaries chosen, in an indistinct unity (see above). Couloubaritsis ingenuously takes Olympus to be Zeus’ mountain, and thus supposes that the earth, with this summit, could reach the astral bodies (why not?), and go beyond, “even, perhaps, [beyond] the Milky Way” (1986:315). Is this serious?

[ back ] 89. The sentence has served to justify the three zones, in certain presentations (see Karsten 1835, above); the rest was read from the perspective of the end.

[ back ] 90. The designation might be common to Parmenides (and Empedocles) and to the Pythagoreans (see Burkert 1962:227n35 [Burkert 1972:244n31]): “an acusma” [TN: a saying attributed, in the Pythagorean community, to Pythagoras himself]; moreover, Burkert resolutely limits the Pythagoreanism of Parmenides in favor of a dependence on Anaximander (see 1962:261n31 [Burkert 1972:282n25 ]: Anaximander—Parmenides—Empedocles).

[ back ] 92. When the heavens are confused with Olympus, that is, the external vault, which is almost always the case, one is obliged to accept a zone of fire that surrounds the universe from the outside. As a way out of this impasse, this transworldly empyrean has been assimilated to Being (see above, p. 200).

[ back ] 93. Gigon (1945:274ff.), without concerning himself with the agreement of the testimonies among themselves, identified in turn the fixed bodies (ether), followed by the sun and the moon (= Anaximenes), then a return to the sky (the vault) for the role attributed to Anankè.

[ back ] 94. Besides A 37, see II.20.8 a = A 43, corroborated by II.5.4 = A 40 a on the order of the astral bodies.

[ back ] 95. The hypothesis, formulated by Bicknell (1968:631), was perhaps more than simply “conceivable” (O’Brien 1967:247n33); it has in its favor the formal elements and the advantage of distinguishing between fragments 10 and 11.

[ back ] 96. See Verdenius 1942:51. The cosmology is given in the form of a cosmogony, by means of a more primitive “narrative exposition.” The explanation of phenomena (Verdenius cites Cornford; see his n. 2) is opposed to the process of genesis, with reference to the different temporal aspects, used in frag. 12.1–2, whereas this genetic process is on the contrary fundamentally interpretive.

[ back ] 97. Cf. Fränkel 1951:412, “the whole sky”; Hölscher 1969:29, “the sky surrounding the rings”; and so on. Most recently, see Cordero’s translations (1984:41) or O’Brien’s (1967:63): “of the heavens that encircle them on all sides” (“them” = “the works of the moon”?) or Couloubaritsis’s: “the heavens that hold them all around.”

[ back ] 98. Let me refer, a bit randomly, given that the opinion is so widely shared, to Tannery (1930:282) and Untersteiner (1958:cxcii, with the references cited, n. 92): “The οὐρανός, which is explained as ὄλυμπος ἔσχατος …”; Coxon (1986:229); and so on.

[ back ] 99. “Necessity” reduced to the obligation to introduce the rampart of a limit against nothingness; see Fränkel 1951:467.

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